Question

Shoe Sizes:

10, 10.5, 11, 11, 7.5, 6.5, 8.5, 9, 10.5, 8, 8, 6, 7.5, 9, 6.5, 7, 6, 10.5, 7.5, 8, 9, 6.5, 8, 7, 12, 6.5, 9.5, 7, 8, 7

Height in inches:

61, 70, 69, 68, 72, 68, 63, 64, 65, 65, 67, 68, 62, 61, 62, 67, 63, 64, 68, 70, 62, 61, 64, 65, 66, 75, 64, 66,, 63, 66, 6

Based on our sample data, is there any linear correlation between our heights and shoe size of all students? Use p-value or critical value method to test the claim there is a linear correlation between heights and shoe size of all college students at a 5% level of significance.

1. Construct Scatterplot. Find the strength, trend, and direction.

2. Perform hypothesis testing to test the claim there is a linear correlation between heights and shoe size of all students at a 5% level of significance.

S1: Find linear coefficient r

S2: The original Claim

S3: Identify Ho and H1

S4: Compute test statistics

S5: Draw the distribution

S6: Find the p-value

S7: What is our statistical conclusion?

S8: State the final words in conclusion.

3. If it has a strong linear correlation, find the regression equation.

4. Estimate a person's shoe size whose height is 55 inches.

5. Predict Sultan Kosen's shoe size

Who is the tallest person in the world?

Sultan Kösen

Sultan Kösen (born 10 December 1982) is a Kurdish public figure, farmer, herder who holds the Guinness World Record for a tallest living male at 251 centimeters (8 ft 2.82 in).

Answer 1

1. The scatterplot is:

There is a weak, negative and linear relationship between the variables.

2. r = -0.046

The hypothesis being tested is:

H₀: = 0

H_a: ≠ 0

Claim: There is a linear correlation between heights and shoe size of all students

The test statistics is -0.245.

The p-value is 0.8083.

Since the p-value (0.8083) is greater than the significance level (0.05), we fail to reject the null hypothesis.

Therefore, we cannot conclude that there is a linear correlation between heights and shoe size of all students.

3. The equation is:

y = 9.7822 - 0.0226*x

4. y = 9.7822 - 0.0226*55 = 8.54

5. y = 9.7822 - 0.0226*98.82 = 7.55